IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v27y2006i1p197-215.html
   My bibliography  Save this article

Bifurcation and chaos in neural excitable system

Author

Listed:
  • Jing, Zhujun
  • Yang, Jianping
  • Feng, Wei

Abstract

In this paper, we investigate the dynamical behaviors of neural excitable system without periodic external current (proposed by Chialvo [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons & Fractals 1995;5(3–4):461–79] and with periodic external current as system’s parameters vary. The existence and stability of three fixed points, bifurcation of fixed points, the conditions of existences of fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using bifurcation theory and center manifold theorem. The chaotic existence in the sense of Marotto’s definition of chaos is proved. We then give the numerical simulated results (using bifurcation diagrams, computations of Maximum Lyapunov exponent and phase portraits), which not only show the consistence with the analytic results but also display new and interesting dynamical behaviors, including the complete period-doubling and inverse period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, simultaneous occurrence of two different routes (invariant cycle and period-doubling bifurcations) to chaos for a given bifurcation parameter, sudden disappearance of chaos at one critical point, a great abundance of period windows (period 2 to 10, 12, 19, 20 orbits, and so on) in transient chaotic regions with interior crises, strange chaotic attractors and strange non-chaotic attractor. In particular, the parameter k plays a important role in the system, which can leave the chaotic behavior or the quasi-periodic behavior to period-1 orbit as k varies, and it can be considered as an control strategy of chaos by adjusting the parameter k. Combining the existing results in [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons & Fractals 1995;5(3–4):461–79] with the new results reported in this paper, a more complete description of the system is now obtained.

Suggested Citation

  • Jing, Zhujun & Yang, Jianping & Feng, Wei, 2006. "Bifurcation and chaos in neural excitable system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 197-215.
  • Handle: RePEc:eee:chsofr:v:27:y:2006:i:1:p:197-215
    DOI: 10.1016/j.chaos.2005.04.060
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905003048
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2005.04.060?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Niu, Ben & Wei, Junjie, 2008. "Stability and bifurcation analysis in an amplitude equation with delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1362-1371.
    2. Xu, Mingtian, 2007. "Property of period-doubling bifurcation cascades of discrete dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 455-462.
    3. Smidtaite, Rasa & Ragulskis, Minvydas, 2024. "Finite-time divergence in Chialvo hyperneuron model of nilpotent matrices," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    4. Chesebro, Anthony G. & Mujica-Parodi, Lilianne R. & Weistuch, Corey, 2023. "Ion gradient-driven bifurcations of a multi-scale neuronal model," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:27:y:2006:i:1:p:197-215. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.